New method for the numerical integration of an N-body system in an external potential

Details New method for the numerical integration of an N-body system in an external potential New method for the numerical integration of an N-body system in an external potential

Jun 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993pasj...45..321e&link_type=abstract

PASJ: Publications of the Astronomical Society of Japan (ISSN 0004-6264), vol. 45, no. 3, p. 321-327.

Statistics

Computation

3

Celestial Mechanics, Computational Astrophysics, Many Body Problem, Numerical Integration, Protoplanets, Solar Gravitation, Gravitational Fields, Orbital Mechanics, Planetary Evolution, Runge-Kutta Method

Scientific paper

A newly developed numerical-integration method is presented. It has a great advantage when used to numerically calculate the orbital motion of mutually interacting planetesimals in a strong external (the solar gravitational) field. In an ordinary difference scheme, since the effect of a weak mutual gravity would be embedded in the truncation error of the strong solar gravity, we cannot reflect the small, but important, effect of mutual gravity on the numerical calculation. Our new method helps us to overcome this difficulty by suppressing the truncation error of numerical integration. The essence of our method is to express a solution as a sum of unperturbed and perturbed solutions: the former represents the motion only under an external field; the latter represents a small deviation from an unperturbed orbit due to mutual gravity between planetesimals. The perturbed solution is found by means of an ordinary integrator, whereas an unperturbed solution is sought by a higher-order integrator (or, by an analytical manner). By this method, we can integrate orbits both accurately and speedily. Since our method has a very simple algorithm, we can apply it to well-known numerical integration methods, such as the Runge-Kutta method and the Predictor-Corrector method.

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